A discarded cigarette found near the body of a 24-year-old US school teacher in her apartment nearly 52 years ago has helped lead investigators to an upstairs neighbour who they say strangled her after having a fight with his wife.

Burlington Police DNA evidence collected from the cigarette butt and dogged investigative work led Vermont authorities to the man they say killed Rita Curran within a 70-minute window on a July night in 1971.

The suspect, identified as William DeRoos, who was 31 at the time and has since died, had left his apartment that night for "a cool-down walk".

After he returned he told his wife of two weeks not to say that he had been out.

Since the investigation was renewed in 2019, detectives re-interviewed Mr DeRoos's former wife.

She told them he had left their apartment for a brief period within a window of time when Ms Curran's roommates were out of her Burlington apartment.

"We're all confident that William DeRoos is responsible for the aggravated murder of Rita Curran, but because he died in a hotel room of a drug overdose he will not be held accountable for his actions, but this case will be closed," Burlington Police detective lieutenant James Trieb, the commander of the Detective Services Bureau, said during a morning news conference on Tuesday.

After Ms Curran's death, Mr DeRoos, who was known to some as a guru, moved to Thailand and became a monk, but he later returned to the US.

Mr DeRoos died of a drug overdose in San Francisco in 1986, police said.

Ms Curran's parents died without learning who had killed their daughter, but the victim's brother and sister attended the event held at Burlington police headquarters.

"I pray to Rita and I pray to my parents."

In the early morning hours of July 20, 1971, Burlington police were called to the Brooks Avenue apartment after Ms Curran's roommate arrived home to find her body in their shared bedroom.

Police say Ms Curran resisted fiercely, but she was strangled. The murder shook Burlington.

The case remained open and investigators never let it go, but in 2019, a team of detectives, officers, technicians and others began working the case as though it had just happened.

A key piece of evidence was a cigarette butt that had been found near Ms Curran's body.

In 2014, previous investigators had sent the butt and other evidence off for DNA analysis. The test did compile a DNA profile of whoever had smoked the cigarette, but it did not match any samples in DNA databases compiled by law enforcement.

The detectives who picked up the case in 2019 contracted with a DNA testing company and the samples were compared with genetic material submitted to commercial DNA testing companies by members of the public.

Last August, Burlington detectives were told the sample, which had been traced through relatives on both sides of Mr DeRoos's family, was pointing at Mr DeRoos, even though he had no DNA profile on record.